Problem: Simplify. Rewrite the expression in the form $b^n$. $b^4\cdot b=$
Solution: $\begin{aligned} b^4\cdot b&=b^4\cdot b^1 \\\\ &=b^{4+1} \\\\ &=b^{5} \end{aligned}$ This follows from the general rule $x^m\cdot x^n=x^{m+n}$. Note that the powers have the same base. We can also see this is correct by expanding the powers. $\begin{aligned} b^4\cdot b&=\underbrace{b\cdot b\cdot b\cdot b}_\text{4 times}\cdot\underbrace{b}_\text{1 time} \\\\\\ &=\underbrace{b\cdot b\cdot b\cdot b\cdot b}_\text{5 times} \\\\ &=b^{5} \end{aligned}$ In conclusion, $b^4\cdot b=b^{5}$.